No Objective Function

In some cases (e.g., design of integrated circuit layouts), the goal is to find a set of variables that satisfies the constraints of the model. The user does not want to optimize anything in particular, so there is no reason to define an objective function. This type of problem is usually called a feasibility problem.

Multiple Objective Functions

Often, the user would actually like to optimize a number of different objectives at once. For instance, in the power plant problem, the objective function is to minimize the operating cost and maximize the power generation quantity simultaneously.

Usually, the different objectives are not compatible; the variables that optimize one objective may be far from optimal for the others. In practice, problems with multiple objectives are reformulated as single-objective problems by either forming a weighted combination of the different objectives or replacing some of the objectives by constraints. These approaches and others are described in the section on multiobjective optimization (see "Optimization procedure two or more variables").

Variables

These are essential. If there are no variables, we cannot define the objective function and the problem constraints.

Constraints

If constraints are not present, this results in the field of unconstrained optimization. In real-life situations, all problems really do have constraints.

Boiler Example

Three boilers B1, B2, and B3 are in operation in a process unit, generating 100,...